Controlled Terahertz Birefringence in Stretched Poly(lactic acid) Films

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Controlled Terahertz Birefringence in Stretched Poly(lactic acid) Films Investigated by Terahertz TimeDomain Spectroscopy and Wide-Angle X-ray Scattering Hotsumi Iwasaki, Madoka Nakamura, Nozomu Komatsubara, Makoto Okano, Masayoshi Nakasako, Harumi Sato, and Shinichi Watanabe J. Phys. Chem. B, Just Accepted Manuscript • Publication Date (Web): 16 Jun 2017 Downloaded from http://pubs.acs.org on June 17, 2017

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The Journal of Physical Chemistry

Controlled Terahertz Birefringence in Stretched Poly(lactic acid) Films Investigated by Terahertz Time-Domain Spectroscopy and Wide-Angle X-ray Scattering Hotsumi Iwasaki1, Madoka Nakamura1, Nozomu Komatsubara1, Makoto Okano1, Masayoshi Nakasako1, Harumi Sato2, and Shinichi Watanabe1*

1. Department of Physics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa 223-8522, Japan.

2. Graduate School of Human Development and Environment, Kobe University, 3-11 Tsurukabuto Nada-ku, Kobe, Hyogo 657-8501, Japan.

*E-mail: [email protected]

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ABSTRACT

We report a correlation between the dielectric property and structure of stretched poly(lactic acid) (PLA) films, revealed by polarization-sensitive terahertz time-domain spectroscopy and two-dimensional (2D) wide-angle X-ray scattering (WAXS). The experiments evidence that the dielectric function of the PLA film becomes more anisotropic with increasing draw ratio (DR). This

behavior

is

explained

by

a

classical

Lorentz

oscillator

model

assuming

polarization-dependent absorption. The birefringence can be systematically altered from 0 to 0.13 by controlling DR. The combination of terahertz spectroscopy and 2D WAXS measurement reveals a clear correlation between the birefringence in the terahertz frequency domain and the degree of orientation of the PLA molecular chains. These findings imply that the birefringence is a result of the orientation of the PLA chains with anisotropic macromolecular vibration modes. Because of a good controllability of the birefringence, polymer-based materials will provide an attractive materials system for phase retarders in the terahertz frequency range.


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1. Introduction

Polymers are one of the most promising materials for optical components in the terahertz frequency range, because of several advantages such as low reflection loss, small weight, and easier mass production compared to that of typical dielectric materials.1,2 At present, lenses,3,4,5windows,3 and beam-splitters1,2,6 made of polymers are widely used as optical components for terahertz spectroscopy. Additional applications of polymers for polarizers,7,8 phase retarders,9,10 and waveguides11 have been proposed as well. In particular, some polymers are known to exhibit a large natural birefringence (∆n~0.2) in the terahertz frequency range.12,13 Such polymers are promising candidates for producing thinner phase retarders compared to the commercially available quartz phase retarders with ∆n~0.05.14 Moreover, it is possible to control the orientation of polymer chains via mechanical deformation such as stretching.15 The large natural birefringence of polymeric materials is usually attributed to a structural anisotropy induced by an orientation of polymer chains or fibers along one direction.12 However, because of the lack of systematic studies on the birefringence of polymers in the terahertz frequency range, the exact relationship between the terahertz birefringence and the structural anisotropy of polymers remains unclear. A better understanding of this relationship is necessary for realizing polymer-based phase-retarders for terahertz spectroscopy.



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There has been a long history of research on birefringence of polymers in the visible frequency range. The relationship of birefringence and the polymer’s anisotropic morphology and crystal structure has been investigated by various techniques, e.g., polarized-Raman spectroscopy,16 nuclear magnetic resonance17 and X-ray diffraction.15,18 However, suitable techniques in the terahertz regime have been developed only recently.13,19-22 It has been demonstrated that terahertz spectroscopy can assess the orientation order and crystal structure of polymers by measuring anisotropic absorption peaks caused by anisotropic macromolecular vibration modes.20,21,23-26 An investigation of the correlation between the anisotropic dielectric properties and structure of polymers by X-ray diffraction will enable us to obtain a deep insight into the physics of terahertz birefringence.

Here, we investigated the spectroscopic and structural properties of stretched poly(lactic acid) (PLA) films by employing terahertz time-domain spectroscopy (THz-TDS) and two-dimensional (2D) wide-angle X-ray scattering (WAXS). We found that the optical anisotropic terahertz response of the stretched PLA films can be described by a sum of dielectric functions of two Lorentz oscillators. One of the oscillators has a polarization parallel to the stretching direction, i.e., the dominant orientation of the polymer chains. Stronger birefringence was observed for stretched PLA films with larger draw ratio (DR), and we were able to control the birefringence ∆ from 0 to 0.13. Furthermore, the 2D WAXS measurement allowed us to 4 ACS Paragon Plus Environment

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find a clear correlation between the terahertz birefringence and the degree of orientation of the crystalline and amorphous phase of the PLA. This information is crucial for practical implementation of these polymers for phase retarders.

2. Materials and methods

Sample preparation

We purchased PLA pellets with an average molecular weight of ~105 (NatureWorks LLC, Ingeo biopolymer 4032D). The melting temperature and the glass transition temperature of the pellets were 150–180 °C and 55–60 °C, respectively. In the first processing step, PLA pellets with a total weight of about 3.3 g were placed on a copper plate that was wrapped in a polyimide film. Before placing the PLA pellets, the wrapped plate was heated by a hot plate at 230 °C. After the heat of the copper plate partly melted the PLA pellets about 10 minutes later, the PLA was sandwiched by another hot copper plate wrapped in a polyimide film. To ensure a complete melting of the PLA, we placed a heated metal with large mass on the copper plates. After 10 minutes, the PLA sample together with the copper plates was quickly immersed in iced water with approximately 0 °C to rapidly quench the PLA far below its glass transition temperature. Finally, a PLA thin film with a diameter of about 90 mm and a thickness of about 0.35 mm was 5 ACS Paragon Plus Environment


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obtained. We cut some PLA films into 18 rectangular samples with a dimension of approximately 15 mm × 25 mm. Two samples were used as reference without drawing. Two other samples were also used as reference samples with two different crystalline phases prepared by isothermal crystallization as explained in the following. One sample was heated at 140 °C for 24 hours to generate the α-crystalline phase. The other sample was heated at 70 °C for 42 hours to grow the α'-crystalline phase27 (see Supporting Information for details).

The other 14 samples were uniaxially drawn by a custom-made mechanical stretching machine. Prior to stretching, a grid pattern was printed on the surface of each sample to measure the DR. The stretching machine consisted of a fixed post and a computer-controlled translation stage. A pair of aluminum blocks with dimensions of 8 mm × 15 mm × 70 mm were attached to the translation stage and the fixed post. Both edges of the short axes of a PLA sample (the 15 mm edges) were clamped by the aluminum blocks on the stage and post. We immersed the sample in hot water at 66 °C, and then stretched it by moving the translation stage with a draw speed of 0.1 m/s. After each drawing process, we quickly immersed the PLA film in water at approximately 25 °C for quenching. The DR is defined with = ⁄ , where and are the initial and final lengths of the center grid lines along the stretching direction, respectively. We prepared 16 samples in total with different DRs between =1.0 and 3.5 (as mentioned


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above, two of them were not stretched, i.e., =1.0). The grid pattern was removed by using ethanol after estimating the DR.

Polarization sensitive terahertz time-domain spectroscopy

We used two experimental setups optimized for different frequency ranges to obtain accurate polarization-dependent spectra over a wide frequency region at room temperature. For the frequency region above 0.8 THz, we built a conventional THz-TDS setup28 by using a mode-locked titanium-sapphire laser, which provides laser pulses with a wavelength of 800 nm, a repetition rate of 80 MHz, a pulse duration of about 100 fs, and an average power of 1 W. The laser pulse train was divided into two beams by a beam sampler for the terahertz pulse generation and detection. One of the beams was used for generating terahertz pulses by optical rectification through focusing it on a 1-mm thick (111)-oriented zinc telluride crystal. The other laser pulse was used for detecting the terahertz pulse by the electro-optic sampling method using a 0.1-mm thick c-cut gallium selenide crystal. The terahertz beam was focused on the stretched PLA sample using two off-axis parabolic mirrors. A wire-grid polarizer (Origin corp., EWG40-Type I) working in the frequency range from 0.8 THz (26 cm-1) to 3.6 THz (120 cm-1) was placed in front of the sample to select the polarization direction of the terahertz beam 7 ACS Paragon Plus Environment


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illuminating the sample. For the frequency region below 0.8 THz (26 cm-1), we used a commercial THz-TDS measurement system (T-ray 5000, Advanced Photonix. Inc.) with a rotating polarizer.29 The beam spot of the terahertz pulse in both experimental setups was approximately about 4 mm, which was sufficiently small compared to the widths of the samples.

Two-dimensional wide-angle X-ray scattering

The 2D WAXS measurements were conducted by using the Cu Kα radiation (λ=1.5418 Å) produced from an Ultrax-18 X-ray generator (Rigaku, Japan) operated at 45 kV and 90 mA. The Cu Kα radiation was selected with a Ni-foil. The diffraction patterns were recorded by an R-AXIS IV detector (Rigaku, Japan) located at a camera distance of 123 mm. The X-ray beam was focused on the detector plane by a set of Pt-coated mirrors (Rigaku, Japan). The exposure time for each PLA film was 60 minutes.

The degree of crystallinity of the stretched PLA samples was estimated by using the summed intensity of the recorded Bragg reflection within the range 11.5° < 2 < 30.3° in the 2D WAXS pattern. For the summation, we distinguished between the tail from the amorphous phase and the peak of the crystalline phase (see Supporting Information for details). The degree of orientation of the crystalline phase of the stretched sample was determined as follows. We 8 ACS Paragon Plus Environment

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first calculated the mean-square cosine of the azimuth angle, , between the crystal axes and stretching direction from the 2D WAXS patterns by using the following equation,15 "

〈cos 〉 ≡

# ! cos sin & " #

, ⋯ 4!

! sin &

where ! is the X-ray intensity of the (200)/(110) reflection at 2 = 16.5°. Then, we defined the degree of orientation + as15

+=

3〈cos 〉 − 1 . ⋯ 5! 2

In our definition, + = −0.5 when the normal axes of the (200) and (110) lattice planes are parallel to the direction perpendicular to the stretching direction, while + = 0 when the crystal axes are randomly oriented15.



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3. Results and discussion

Draw ratio dependence of the anisotropic dielectric functions of stretched PLA films at terahertz frequency range

We first investigated the dielectric functions of the 16 PLA samples at terahertz frequencies (ranging from 26 to 120 cm-1) using a polarization-sensitive THz-TDS system. In the case of the unstretched samples, we defined the stretching direction with the longer edge of the rectangle. Figure 1 shows the complex dielectric functions of the PLA samples parallel (a and b)

Figure 1. Dielectric functions (a),(b) parallel and (c),(d) perpendicular to the stretching direction of the PLA samples. The real and imaginary parts are shown in the top and bottom panels, respectively. Experimental data are shown with the symbols and fitted by theoretical predictions (solid lines). The details are described in the main text. 10 ACS Paragon Plus Environment

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and perpendicular (c and d) to the stretching direction. Figures 1a and c correspond to the real part (-′), while Figure 1b and d correspond to the imaginary part (-′′). Both -′ and -′′ of the unstretched sample are independent of the direction. This finding implies that the dielectric function of the unstretched sample is isotropic, probably because there is no structural anisotropy. With regard to the spectroscopic features of the unstretched sample, - / gradually decreases as the frequency increases, while -′′ has a broad peak around 54 cm-1. This peak is consistent with the result reported by Fuse et al.23 They attributed the broad peak of -′′ to the absorption peak of the accordion-like modes.30

On the other hand, the stretched samples exhibit a clear directional dependence for both - / and -′′, which means that the dielectric responses of the stretched samples have a remarkable large anisotropy in the terahertz frequency region. As the DR increases, - / parallel (perpendicular) to the stretching direction increases (decreases) below 60 cm-1, and -′′ parallel (perpendicular) to the stretching direction increases (decreases) at 54 cm-1. Because the polymer chains are oriented along the stretching direction,31 the anisotropic optical responses has been observed in the stretched polymeric materials at the terahertz frequency region.21 Thus, we considered that the observed anisotropy most likely originates from the anisotropic absorption in the oriented PLA molecular chains. Indeed, Fuse et al.23 have calculated that the absorption peak frequency of the lactide oligomer for a probe light polarized parallel to its helical axis is lower 11 ACS Paragon Plus Environment


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compared to that for perpendicular polarization. Our experimental observations shown in Figure 1 qualitatively agree with their numerical prediction.

In order to further understand the DR dependence of the dielectric function in the PLA films, we assumed that there exist two absorption peaks for the PLA film sample. We fitted the parallel and perpendicular components of the dielectric function of the stretched PLA films by a sum of two classical Lorentz oscillators as follows,32 03 − 0 ! 0 − 0 ! + 2 ∙ , ⋯ 1! 03 − 0 ! + 53 0! 0 − 0 ! + 5 0! 53 0 5 0 -′′ 0! = 23 ∙ + 2 ∙ , ⋯ 2! 03 − 0 ! + 53 0! 0 − 0 ! + 5 0! -′ 0! = -∞ + 23 ∙

where 03 and 0 are the resonant angular frequencies of the two Lorentz oscillators with the damping rates 53 and 5 , respectively. 23 and 2 are the so-called plasma frequencies in the classical Lorentz oscillator model.32 -∞ is a background dielectric constant. We performed a global fitting of the sixty-four (4 × 16) spectral data, i.e., the real and imaginary parts of the dielectric functions parallel and perpendicular to the stretching direction for all 16 samples, by using eqs 1 and 2 with the shared parameters 03 , 0 , 53 and 5 . The fitting curves (shown in Figure 1) are in agreement with the experimental data, implying that the simple two-oscillator model is sufficient to explain the observed frequency-dependent variation of the dielectric functions in the stretched PLA films. 12 ACS Paragon Plus Environment

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Table 1. Parameters of the Lorentz model described by eqs 1 and 2 obtained from the fitting to the experimental data in Figure 1. Parallel (//) means that the polarization is parallel to the stretching direction. Perpendicular ( ⊥) corresponds to the polarization normal to the stretching direction.

Direction

ω3 ω γ γ ; 2π! ; 2π! 3; 2π! ; 2π!

23

2

(cm-1)

(cm-1)

1.0

82

280

2.3

3.4

180

220

2.5

1.0

83

280

2.3

3.4

0

280

2.3

DR

(cm-1)

(cm-1)

(cm-1)

(cm-1)

ε>

// 53

76

29

93

⊥

Table 1 summarizes the fitting parameters for = 1.0 and 3.4. The two resonant frequencies 03 /28 and 0 /28 are at 53 and 76 cm-1, respectively. Note that 23 is zero for = 3.4 in case that the polarization of the probe light is perpendicular to the stretching direction, whereas it has almost the same value of 82 cm-1 for both directions in the sample with = 1. Figure 2 shows the detailed DR dependence of the plasma frequencies 23 and 2 along the two polarization directions. We found that 23 in the parallel direction gradually increases with increasing DR, but decreases in the perpendicular direction. This result indicates that the absorption at 53 cm-1 is caused by molecular vibration whose polarization is almost along the 13 ACS Paragon Plus Environment


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Figure 2. Draw ratio dependence of the fitting parameters (a) 23 and (b) 2 , with their parallel and perpendicular components shown with circles and triangles, respectively.

direction of PLA chains (=stretching direction). This consideration is consistent with Fuse's prediction that one of the absorption band in 50 cm-1 is due to the molecular vibration along the helical axis of PLA chains.23 On the other hand, 2 shows a relatively weak dependence on the DR. This fact suggests that the Lorentz oscillator with the resonance frequency of 76 cm-1 consists of several molecular vibration modes with various polarization dependences, resulting in a low polarization sensitivity. Further investigations are required to understand the origin of this oscillator.


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Controlled terahertz birefringence in stretched PLA films

The real (n) and imaginary parts (k) of the complex refractive indices ( + AB = √- ′ + A- ′′ ) of the PLA sample for =3.4, analyzed with respect to parallel (∥ and B∥ ) and perpendicular (E and BE ) to the stretching direction are plotted in Figure 3. The real part of the refractive index depends on the stretching direction; for frequencies below 03 (and also in the region above 0 ) we found that ∥ is larger than E, while it is slightly smaller in the range

Figure 3. (a) Real and (b) imaginary parts of the complex refractive indices for both directions, measured on the sample with DR =3.44. (c) Birefringence as a function of frequency for the same sample. 15 ACS Paragon Plus Environment


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between 03 and 0 . Furthermore, B∥ has a large peak at 03 , and BE has a broad peak centered around 0 . These characteristic spectral features support our assumption that the dielectric functions obey the classical Lorentz oscillator model. Figure 3c shows the birefringence ∆ = ∥ − E as a function of the wavenumber of the incident terahertz wave. ∆ is negative between 03 and 0 . In contrast, ∆ has a large positive value in the frequency range smaller than 03 and is also nearly constant in the range from 10 to 40 cm-1.

To explore the possibility of controlling the terahertz birefringence by stretching of the PLA sheet, we investigated the correlation between the birefringence ∆ of the stretched PLA sample and the DR. Figure 4a shows the DR dependence of ∆ at terahertz frequencies corresponding to 16.7 and 39.0 cm-1. Under this condition, ∆ is almost proportional to DR–1. Since the DR can be controlled by our custom-made stretching machine, the trend observed in Figure 4 provides a reference curve to produce stretched PLA films with a desired ∆. We note that the anisotropy of the imaginary part of the refractive index, ∆B = B∥ − BE , is small below 33 cm-1, which is lower than the two resonance frequencies, and thus enables application of stretched PLA films as phase retarders at lower terahertz frequency ranges.


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Figure 4. (a) DR dependence of the birefringence at 16.7 cm-1(red filled circles) and 39.0 cm-1(blue open circles). WAXS patterns for samples with three different DRs are also shown. (b) DR dependence of the degree of crystallinity. (c) DR dependence of the degree of the PLA chain orientation.

Correlation between the birefringence and structure of stretched PLA films revealed by a combination of terahertz spectroscopy and 2D WAXS measurement

So far, we confirmed that the stretching technique is useful to induce an anisotropic change in the refractive index. However, the understanding of the underlying physical mechanism is important for the industrial design of optical components. To unveil the relationship between the terahertz optical responses and macromolecular structure of polymeric 17 ACS Paragon Plus Environment


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materials, a combination of the terahertz spectroscopy and WAXS measurements are quite useful.21 Therefore, in addition to the THz-TDS, we investigated the crystal phase, degree of crystallinity, and degree of orientation of the PLA samples by 2D WAXS measurements. Figure 4a shows the 2D WAXS patterns of the PLA samples with =1.0 (unstretched), 2.6 and 3.4. The 2D WAXS pattern of the unstretched sample exhibits a diffuse and isotropic halo. This indicates that the unstretched PLA sample is in an amorphous phase with random orientations of the polymer chains. On the other hand, the 2D WAXS pattern of the stretched PLA samples shows several strong diffraction peaks, indicating that the sample was partly crystallized by the mechanical stretching process.31 It has been reported that PLA sheets can contain several crystalline phases (so-called α- and α'-phases), mixed with the amorphous phase. The diffraction peaks oriented in the equatorial (horizontal) direction are observed at a diffraction angle 2θ = 16.5° (corresponding to a diameter of 50% of the image size), which indicate the formation of the crystalline α'-phase16 and its orientation along the stretching direction. We would like to emphasize that the birefringence is determined by the orientation of both crystalline and amorphous phases, and thus it is not possible to separate their contributions with the THz measurement alone. The 2D WAXS provides additional information on the orientation of the crystalline phase. We estimated the degree of crystallinity, G, and degree of orientation of the crystalline α'-phase of the samples, +, from the 2D WAXS patterns. In our definition, + = 0 18 ACS Paragon Plus Environment

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when the crystal axes are randomly oriented, and + = −0.5 when the PLA molecular chains in the crystalline α'-phase are perfectly aligned along the stretching direction. Figure 4b and 4c show the DR dependence of G and +, respectively. We found that both G and |+| increase as DR increases.

Next, we discuss the relationship between the birefringence (∆), the degree of crystallinity (G), and the degree of orientation of the crystalline phase (+) to understand how the optical anisotropy in the terahertz frequency range is caused by the underlying structural anisotropy. As mentioned above, we consider that the birefringence, induced by mechanical stretching, originates from the anisotropic absorption caused by ordered orientation of the PLA molecular chains. From Figures 4a and c we may infer that the increase of ∆ is related to the increase of |+|. However, the dielectric functions of the α'-crystalline and amorphous phases in the PLA samples are almost the same in the terahertz frequency region (see Supporting Information). Therefore, the birefringence ∆ determined by the THz-TDS can contain contributions from both crystalline and amorphous phases of the polymer chains. It is important to note that +, which was determined by the 2D WAXS measurements, describes the orientation of polymer chains in the crystalline phase only. Therefore, we can derive information on the orientation of the polymer chains even for the amorphous phase by a combination of the THz-TDS and the 2D WAXS measurements. At small DR ( < 2), the degree of crystallinity 19 ACS Paragon Plus Environment


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G is almost zero (i.e., crystalline chains hardly exist), while ∆ increases nearly proportional to − 1. This result indicates that, at small DR, the polymer chains in the amorphous phase are gradually oriented along the stretching direction as the DR increases. Thus, the degree of orientation of the amorphous polymer chains govern the birefringence ∆ at small DR. As the DR further increases, the degree of crystallinity gradually increases due to strain-induced crystallization.31 At large DR ( ~ 3.4), + is close to −0.5, indicating that almost all molecular chains in the crystalline phase are oriented along the stretching direction. Moreover, the optical absorption at 03 is reduced to zero at ~ 3.4 when the polarization is perpendicular to the stretching direction (Figure 2 a). These experimental results suggest that for ~ 3.4, the polymer chains in both the crystalline and amorphous phases are almost oriented along the stretching direction.

Finally, we discuss the practical benefits and drawbacks of using stretched PLA as phase retarders in optical components. First, we list up several advantages. PLA is widely-used as a thermoplastic material for 3D printing.33 PLA can be also easily stretched in hot water above 60 °C and the birefringence is well controlled by changing the DR. The stretched PLA samples show a large birefringence with a low mean refractive index (I ≡

J∥ KJL

=1.66) as shown in

Figure 3 a. These features are suitable for realizing thin phase retarders with low reflection loss and easy mass production. On the downside, we found that the stretched PLA samples have a 20 ACS Paragon Plus Environment

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relatively large absorption loss of the incident light although the linear dichroism (∆B) is small. The absorption coefficient is 8.4 cm-1 at a frequency of 16.7 cm-1 (0.5 THz), which is larger than that of phase retarders with artificial dielectric gratings based on form birefringence.34 In this article, we found that the large birefringence of the polymer in the terahertz frequency region can be explained by the classical Lorentz oscillator model. We believe that our findings represent a general feature for this kind of polymeric materials. In fact, there exists a polymer which has an absorption peak at higher frequency region, which might be a good candidate for a phase retarder with low absorption loss at low terahertz frequency range.20 We consider that further experimental investigations enable realization of polymer-based phase retarders for practical use.

4. Conclusion

In conclusion, we performed a detailed study of terahertz birefringence in stretched PLA films by using polarization-sensitive THz-TDS and 2D WAXS measurements. The origin of the terahertz birefringence is assigned to the anisotropic molecular vibration modes in the terahertz frequency range, which can be described by the classical Lorentz oscillator model. In addition, we clearly demonstrated that the birefringence can be systematically altered by controlling the DR of the PLA samples. With the 2D WAXS measurements we clarified that a stronger 21 ACS Paragon Plus Environment


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birefringence appears in the PLA layer with a higher degree of orientation of the crystalline phases, but under certain conditions the amorphous phase can also play an important role. This observation helps to associate the anisotropy in optical birefringence with the structural anisotropy of the stretched PLA. Further detailed spectroscopic studies with combination of macromolecular structural studies of polymer films will provide novel knowledge for designing and fabricating polymer-based phase retarders in the terahertz frequency region with small weight, low cost, and easy mass production.


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AUTHOR INFORMATION

Corresponding Author * (SW). E-mail: [email protected], Phone: +81-45-566-1687.

Notes The authors declare no competing ﬁnancial interest.

ACKNOWLEDGMENT Part of this work was supported by Japan Science and Technology Agency (JST) under Collaborative Research Based on Industrial Demand “Terahertz-wave: Towards Innovative Development of Terahertz-wave Technologies and Applications”, and a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science, and Technology, Japan for the Photon Frontier Network Program.

ASSOCIATED CONTENT



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Supporting Information.

2D WAXS patterns (Figures S1) and complex dielectric spectra in the terahertz frequency range (Figures S2) of unstretched PLA film samples with different heat treatments; an amorphous sample with no heat treatment, a sample annealed at 140 ºC for 24 h, and a sample annealed at 70 ºC for 42 h. The method for estimating the degree of crystallinity of the stretched PLA samples from the 2D WAXS pattern (Figure S3).

ABBREVIATIONS PLA,

poly(lactic

acid);

THz-TDS,

terahertz

time-domain

two-dimensional wide-angle X-ray scattering; DR, draw ratio.


spectroscopy;

2D-WAXS,

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Table of Contents Graphic


0.15

Δn at 16.7 cm-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

0.10

0.05

The Journal of Physical ChemistryPage 32 of 36

3.4

DR=1.0

2.6

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3.5

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ε'

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

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(b)

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DR 1.0 1.9 2.6 3.4

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ε'

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200 150


300

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200

a2 (cm-1)

a1 (cm-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

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1.8 1.7 1.6 1.5 0.3 0.2

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

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f

(a)

The Journal of Physical Chemistry 25

2.0 2.5 3.0 Draw ratio

3.5

Controlled Terahertz Birefringence in Stretched Poly(lactic acid) Films

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